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1.
Unified analytical solutions to two-body problems with drag   总被引：3，自引：0，他引：3  
The two-body problem with a generalized Stokes drag is discussed. The drag force is proportional to the product of the velocity vector and the inverse square of the distance. The generalization consists of allowing two different proportionality constants for the radial and the transverse components of the force. Under the 'generalized Robertson transformation', the equation of the orbit takes the form of the Lommel equation and admits solutions in terms of Bessel and Lommel functions. The exact, analytical solutions for this type of drag reveal a paradoxical effect of increasing eccentricity for all trajectories. The Poynting–Robertson drag and Poynting–Plummer–Danby problems are discussed as particular cases of the general solution.  相似文献   

2.
A complete solution is given for a symmetric case of the problem of the planar central configurations of four bodies, when two bodies are on an axis of symmetry, and the other two bodies have equal masses and are situated symmetrically with respect to the axis of symmetry. The positions of the bodies on the axis of symmetry are described by angle coordinates with respect to the outside bodies. The solution is such, that giving the angle coordinates, the masses for which the given configuration is a central configuration, can be computed from simple analytical expressions of the angles. The central configurations can be described as one-parameter families, and these are discussed in detail in one convex and two concave cases. The derived formulae represent exact analytical solutions of the four-body problem.  相似文献   

3.
An exact solution for the Stokes problem for an infinite vertical plate has been derived on taking into account the constant heat flux at the plate. It has been observed that the velocity of the fluid increases with increasingt (time) orG (the Grashof number).  相似文献   

4.
In this communication we present an analytical model for the restricted three-body problem, in the case where the perturber is in a parabolic orbit with respect to the central mass. The equations of motion are derived explicitly using the so-called Global Expansion of the disturbing function, and are valid for any eccentricity of the massless body, as well as in the case where both secondary masses have crossing orbits. Integrating the equations of motion over the complete passage of the perturber through the system, we are then able to construct a first-order algebraic mapping for the change in semimajor axis, eccentricity and inclination of the perturbed body.Comparisons with numerical solutions of the exact equations show that the map yields precise results, as long as the minimum distance between both bodies is not too small. Finally, we discuss several possible applications of this model, including the evolution of asteroidal satellites due to background bodies, and simulations of passing stars on extra-solar planets.  相似文献   

5.
Binary systems showing both apsidal motion and light travel time (LTT) effects which cause orbital period changes in close binaries were studied. 15 triple systems showing apsidal motion were found by searching the literature, and a table including the important parameters of these systems was constructed. Six of the systems given in this table were selected and observed photometrically. Existence of both apsidal motion and LTT effects in all selected systems was investigated by means of the analysis of their eclipse times. The mean observed internal structure constants,  log = k 2,obs  , and contributions to the apsidal motion from the theory of General Relativity and the third/fourth bodies were calculated. The masses of the third/fourth bodies and some characteristics of their orbits were also calculated.  相似文献   

6.
The development of effective iterative methods capable of accurately solving NLTE Stokes transfer problems is of considerable importance for the investigation of solar and stellar magnetic fields. After briefly indicating the iterative approach which is being presently pursued for the exact solution of such problems, the particular regime where polarization signals can only be due to the Zeeman effect is considered in some detail. By means of NLTE Stokes transfer calculations for a two-level atomic model it is first shown that the currently-used field-free approximation (Rees, 1969) cannot be safely applied in the presence of magnetic field gradients. Such gradients lead to changes in the shape and width of the line profiles and they can produce non-negligible effects on the atomic level populations and line source functions. A new approximate method is then proposed, which does not require the actual solution of the Stokes vector transfer equation and is practically as fast as the field-free one. This polarization-free approximation provides a fairly good account of the effects of homogeneous and inhomogeneous magnetic fields on the statistical equilibrium and is very easy to implement in any existing non-magnetic, multi-level transfer code.On leave from the Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, Largo E. Fermi 5, I-50125 Firenze, Italia  相似文献   

7.
An exact cosmological solution for Friedman Robertson Walker (FRW)metric is obtained with a classical scalar field φ along with a potential in the presence of a causal viscous fluid. Assuming the scale factor to be a function of the scalar field we have obtained solutions in both the truncated and the full causal theory. It is shown that an inflationary model can be obtained by imposing certain constraints on some constants. The radiative bulk viscosity during the decoupling era has also been studied as a special case. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

8.
Secular Love numbers of the major planets have been determined by solving the first (Dirichlet's) boundary — value problem for the level ellipsoid as the boundary surface. It has been demonstrated that the rotational distortions are responsible for the actual figure of the bodies above. The 6th degree Stokes zonal parameter for Uranus and for Neptune have been predicted.  相似文献   

9.
The exact definition of the tidal potential is given on the basis of the theory of the restricted three-body problem. There are no limitations as regards the perturbing terms in the gravitational fields of the tide forming bodies; andno a priori conditions are needed in the definition.  相似文献   

10.
Regions of possible motions are established for dynamical systems possessing time-independent Hamiltonians or for systems which are reducible to that form by means of integrals of the motion using only extended point transformations. The method is applied to the problem of three bodies in a plane and surfaces of zero velocity are found. The governing parameters are the energy, angular momentum and the masses of the participating bodies. The analytical and geometrical properties of these surfaces provide qualitative results for given constants of the motion.  相似文献   

11.
The topic of magnetic field diagnostics with the Zeeman effect is currently vividly discussed. There are some testable inversion codes available to the spectropolarimetry community and their application allowed for a better understanding of the magnetism of the solar atmosphere. In this context, we propose an inversion technique associated with a new numerical code. The inversion procedure is promising and particularly successful for interpreting the Stokes profiles in quick and sufficiently precise way. In our inversion, we fit a part of each Stokes profile around a target wavelength, and then determine the magnetic field as a function of the wavelength which is equivalent to get the magnetic field as a function of the height of line formation.To test the performance of the new numerical code, we employed “hare and hound” approach by comparing an exact solution (called input) with the solution obtained by the code (called output). The precision of the code is also checked by comparing our results to the ones obtained with the HAO MERLIN code. The inversion code has been applied to synthetic Stokes profiles of the Na D1 line available in the literature. We investigated the limitations in recovering the input field in case of noisy data. As an application, we applied our inversion code to the polarization profiles of the Fe i λ 6302.5 Å observed at IRSOL in Locarno.  相似文献   

12.
Two formal solutions of the radiative transfer equation for polarized light have been proposed. One uses the Stokes parameters to describe the polarization, while the other uses the coherency matrix. It is shown in the present work that they are equivalent. Both can be used to compute response and contribution functions for the Stokes parameters and both require the solution of systems of differential equations with similar numbers of independent variables. New equations to solve the radiative transfer problem using the Stokes parameters formalism are presented. In addition, a computer code which synthesizes the Stokes profiles by means of these equations is described.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

13.
A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part of this Hamiltonian via the Hamilton–Jacobi equation provides the action-angle variables that ease the construction of a perturbation solution by Lie transforms. The lowest orders of the transformation equations of the perturbation solution are checked to agree with Kinoshita’s corresponding expansions for the exact solution of the free rigid body problem. For approximately axisymmetric bodies rotating close to the principal axis of maximum inertia, the common case of major solar system bodies, the new approach is advantageous over classical expansions based on a small triaxiality parameter.  相似文献   

14.
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15.
In this paper we study the effects of short-period perturbations in the planar asteroidal problem with Stokes drag. The averaging of the dissipative terms is extended to show the appearance of crossed-terms which, in most commensurabilities, are more important than several zeroth-order terms calculated in previous works. In the case of resonance trapping in a libration point, we also discuss the effects of the eccentricity of the perturber in the stationary solution. For the so-called ‘universal eccentricity’, we show that the contributions due to both, short-period terms and harmonics of the auxiliary resonant angle, lead to a corrected value which is no longer invariant. The most significant dependence of this new librational eccentricity is with the eccentricity of the perturber, although a slight variation is also noted with respect to the chosen drag coefficient. In all cases, we present comparisons with numerical simulations of the exact N-body equations. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

16.
The results of photometric and polarimetric observations carried out for some bright atmosphere-less bodies of the Solar system near the zero phase angle reveal the simultaneous existence of two spectacular optical phenomena, the so-called brightness and polarization opposition effects. In a number of studies, these phenomena were explained by the influence of coherent backscattering. However, in general, the interference concept of coherent backscattering can be used only in the case where the particles are in the far-field zones of each other, i.e., when the scattering medium is rather rarefied. Because of this, it is important to prove rigorously and to demonstrate that the coherent backscattering effect may also exist in densely packed scattering media like regolith surface layers of celestial bodies. From the results of the computer modeling performed with the use of numerically exact solutions of the macroscopic Maxwell equations for discrete random media with different packing densities of particles, we studied the origin and evolution of all the opposition phenomena predicted by the coherent backscattering theory for low-packing-density media. It has been shown that the predictions of this theory remain valid for rather high packing densities of particles that are typical, in particular, of regolith surfaces of the Solar system bodies. The results allow us to conclude that both opposition effects observed simultaneously in some high-albedo atmosphereless bodies of the Solar system are caused precisely by coherent backscattering of solar light in the regolith layers composed of microscopic particles.  相似文献   

17.
We present the results of studying the impact linear polarization of 32 solar flares of X-ray classes C, M, and X (two flares) observed with the Large Solar Vacuum Telescope. It has turned out that there is evidence for impact polarization only in 13 of them. The newly obtained data have confirmed that the linear Stokes parameters are predominantly 2–7%, while the spatial sizes of flaring points with nonzero Stokes parameters are small (1″-2″). Two features of the manifestation of impact polarization in flares revealed by these studies are of greatest interest: (1) at the two foot points of a single flare loop or an arcade of loops, both the Hα intensity profiles and the Stokes profiles differ in behavior; (2) based on the Hα line, we have found for the first time that the sign of the Stokes parameters changes not only across the flare ribbon but also with depth of the chromosphere.  相似文献   

18.
The problem of fundamental physical constants variability is discussed on the basis of extended conformal symmetry principles including the concept of local mass variability. It is shown, in particular, that the canonical determination of conformal weights can lead, in general, to non-invariance of the known elementary charge-to-mass ratio. The introduction of active time-like and space-like conformal transformations leads also to possibility of simultaneous variations of dimensional constants without any observable changes in the evolution of the Univrse. The generally covariant method of space-time splitting for conformal renormalization of the metric is considered in terms of Lie derivatives.  相似文献   

19.
Consider a system of two rigid, massive bodies interacting according to their mutual gravitational attraction. In a relative equilibrium motion, the bodies rotate rigidly and uniformly about a fixed axis in \({\mathbb {R}}^3\). This is possible only for special positions and orientations of the bodies. After fixing the angular momentum, these relative equilibrium configurations can be characterized as critical points of a smooth function on configuration space. The goal of this paper is to use Morse theory and Lusternik–Schnirelmann category theory to give lower bounds for the number of critical points when the angular momentum is sufficiently large. In addition, the exact number of critical points and their Morse indices are found in the limit as the angular momentum tends to infinity.  相似文献   

20.
The Advanced Space-based Solar Observatory(ASO-S) mission aims to explore the two most spectacular eruptions on the Sun: solar flares and coronal mass ejections(CMEs), and their magnetism.For the study of CMEs, the payload Lyman-alpha Solar Telescope(LST) has been proposed. It includes a traditional white-light coronagraph and a Lyman-alpha coronagraph which opens a new window to CME observations. Polarization measurements taken by white-light coronagraphs are crucial for deriving fundamental physical parameters of CMEs. To make such measurements, there are two options for a Stokes polarimeter which have been applied by existing white-light coronagraphs for space missions. One uses a single or triple linear polarizer, the other involves both a half-wave plate and a linear polarizer. We find that the former option is subject to less uncertainty in the derived Stokes vector propagating from detector noise.The latter option involves two plates which are prone to internal reflections and may have a reduced transmission factor. Therefore, the former option is adopted as our Stokes polarimeter scheme for LST. Based on the parameters of the intended linear polarizer(s) colorPol provided by CODIXX and the half-wave plate 2-APW-L2-012 C by Altechna, it is further shown that the imperfect maximum transmittance of the polarizer significantly increases the variance amplification of Stokes vector by at least about 50% when compared with the ideal case. The relative errors of Stokes vector caused by the imperfection of colorPol polarizer and the uncertainty due to the polarizer assembly in the telescope are estimated to be about 5%. Among the considered parameters, we find that the dominant error comes from the uncertainty in the maximum transmittance of the polarizer.  相似文献   

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